Providing a decimal time is a straightforward issue.
First we observe, that a day consists of 24 times 60 times 60 =
86,400 seconds.
Then we need to find a smallest time increment which is close enough to the
second familiar to us, and which still fits into a decimal system.
A sensible choice is 0.864 seconds, representing 1/100,000 of a day.

By defining, that a day begins at midnight also for the decimal time,
we have time 0 at midnight, time 1 a mere 0.864 seconds later, time 25,000
at 6:00 am, time 50,000 at noon, time 75,000 at 6:00 pm, and time 99,999
a tiny 0.864 seconds before midnight.

img/flipclock/0.pngA changing digit in flip clock look

Hora2.4 h

img/flipclock/0.pngA changing digit in flip clock look

Prima14.4 min

img/flipclock/0.pngA changing digit in flip clock look

Secunda1.44 min

img/flipclock/0.pngA changing digit in flip clock look

Tertia8.64 s

img/flipclock/0.pngA changing digit in flip clock look

Quarta0.864 s

Note, that the accuracy of this digital clock is bound to your
computer time: it is a direct reflection of it. If your clock is wrong,
than this one is as well.

A little bit of Javascript does what we want. For the representation of
the decimal time ordinary digits would do, of course, but I was explicitely in
search for some flip clock digits. Just when I was about to give up,
I came across the page of http://web.media.mit.edu/~guy/blog/entry.php?14070701Guy Hoffman
, in which he makes his designed digits public. I resized them to suit
my needs, and to the right you can see the result. Of course,
this derivative work is public as well.

All what's left to do is to provide some fancy names so that we can avoid
speaking of 5 digit numbers most of the time.

So let's look at the meaning of "minute" and "second"
for an instant. The term "minute" comes from (lat.)
pars minuta prima,
i.e. the first subdivision (namely of an hour,
into 60 parts). Likewise, the term "second" comes from (lat.)
pars minuta secunda,
i.e. the second subdivision (namely the subdivision
of the first subdivision, hence of a minute,
again into 60 parts).

If we go with the system, we'd name the leftmost digit hora (lat. for hour),
followed by prima (rather than the inconsistent minuta) and
secunda
(both for 10 parts rather than 60).
Then we may come up easily with two further names for the missing digits,
namely pars minuta tertia and pars minuta quarta. dash
Of couse, nothing stops you from calling the second and third digit a
"minute" (of which 100 make an hour) and the rightmost two digits
"second" (of which 100 make a minute). This would also have the
advantage of being easily represented by clocks with 3 hands, not much
different than those in use today.

As a side note, the first 3 digits of decimal time correspond to the number of
.beats in the
Swatch Internet Timehttp://en.wikipedia.org/wiki/Swatch_Internet_Time
. The two last digits are unofficially named centibeats.